Ordering Garside groups

Abstract : We introduce a structure on a Garside group that we call Dehornoy structure and we show that an iteration of such a structure leads to a left-order on the group. We define two conditions on a Garside group G and we show that if G satisfies these two conditions, then G has a Dehornoy structure. Then, we show that the Artin groups of type A and of type I2(m), m≥4 satisfy these conditions, and therefore have Dehornoy structures. As indicated by the terminology, one of the orders obtained by this method on the Artin groups of type A coincides with the Dehornoy order.
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https://hal-univ-bourgogne.archives-ouvertes.fr/hal-02194489
Contributeur : Imb - Université de Bourgogne <>
Soumis le : jeudi 25 juillet 2019 - 15:27:17
Dernière modification le : vendredi 26 juillet 2019 - 01:27:48

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Diego Arcis, Luis Paris. Ordering Garside groups. International Journal of Algebra and Computation, World Scientific Publishing, 2019, 29 (05), pp.861-883. ⟨https://www.worldscientific.com/doi/10.1142/S0218196719500322⟩. ⟨10.1142/S0218196719500322⟩. ⟨hal-02194489⟩

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